The Analytic Adventures of ez: Siegel’s Lemma and the transcendence of eπ
  • Edward B. Burger
  • Robert Tubbs


In the previous two chapters we exploited the simplicity of the power series for the function e z in order to establish the transcendence results of Hermite-Lindemann and then Lindemann-Weierstrass. In this chapter we describe the next stage in the evolution of classical transcendental number theory, which involves viewing e z as a function of a complex variable z and applying more sophisticated analytic techniques. We illustrate these new themes by establishing the transcendence of e π .


Power Series Entire Function Rational Number Algebraic Number Integer Solution 
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Copyright information

© E.B. Burger and R. Tubbs 2004

Authors and Affiliations

  • Edward B. Burger
    • 1
  • Robert Tubbs
    • 2
  1. 1.Department of MathematicsWilliams CollegeWilliamstownUSA
  2. 2.Department of MathematicsUniversity of Colorado at BoulderBoulderUSA

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